Finite Group Databasebeta

← C59×#18190 #28430299

Subgroups — C59×#18190 #28430299

Order 15104.

1126 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3506C211yesmaximal, characteristic, complemented
2C59×#3110C211yesmaximal, characteristic, complemented
3C59×#3109C211yesmaximal, characteristic, complemented
4C59×#2397C211yesmaximal, characteristic, complemented
5C59×#1618C214yesmaximal, complemented
6C59×#1600C214yesmaximal, complemented
7C59×#1506C211yesmaximal, characteristic, complemented
8C59×#1505C211yesmaximal, characteristic, complemented
9C59×#1466C211yesmaximal, characteristic, complemented
10C59×#559—22no—
11C59×#556—21no—
12C59×#555—21no—
13C59×#553—22no—
14C59×#550—21no—
15C59×#547—21no—
16C59×#538C2214yes—
17C59×#535—21no—
18C59×#533C2211yescharacteristic
19C59×#532C2211yescharacteristic
20C59×#525—22no—
21C59×#520—21no—
22C2×C4×D4×C59—22no—
23C2×C4×D4×C59C2211yescharacteristic
24C2×C4×D4×C59C2211yescharacteristic
25C59×#484C2212yes—
26C59×#481C2212yes—
27C59×#476—21no—
28C59×#474—21no—
29C59×#461—21no—
30C59×#459—21no—
31C59×#450C2212yes—
32C59×#447C2212yes—
33C59×#442—22no—
34C59×#440—22no—
35C59×#432C2211yescharacteristic
36C59×#432C2211yescharacteristic
37C59×#399—21no—
38C59×#399C2212yes—
39C59×#392—21no—
40C59×#392C2212yes—
41C59×#376C2211yescharacteristic
42C59×#328C2214yes—
43C59×#327C2214yes—
44C59×#323C2214yes—
45C2×#41×C59—22no—
46C2×#41×C59—21no—
47C22×D4×C59—22no—
48C22×D4×C59D411yescharacteristic
49C22×D4×C59C2311yescharacteristic
50C23×C4×C59—21no—
51C23×C4×C59D412yes—
52C2×SD16×C59—22no—
53C2×D8×C59—22no—
54C4⋊Q8×C59D411yescharacteristic, complemented
55C4⋊Q8×C59D411yescharacteristic, complemented
56C4⋊Q8×C59D411yescharacteristic, complemented
57#127×C59—22no—
58#127×C59D411yescharacteristic, complemented
59#126×C59—24no—
60#125×C59—21no—
61#124×C59—22no—
62#124×C59—24no—
63#124×C59—21no—
64#123×C59—24no—
65#123×C59—24no—
66C22⋊Q8×C59—22no—
67C22⋊Q8×C59—21no—
68C22⋊Q8×C59C2312yes—
69#121×C59—22no—
70#121×C59—22no—
71#121×C59—22no—
72#121×C59—24no—
73#121×C59—21no—
74#121×C59C2312yes—
75#120×C59—24no—
76C4×Q8×C59—22no—
77C4×Q8×C59—21no—
78C4×Q8×C59D412yescomplemented
79C4×D4×C59—22no—
80C4×D4×C59—24no—
81C4×D4×C59—24no—
82C4×D4×C59—21no—
83C4×D4×C59—21no—
84C4×D4×C59—21no—
85C4×D4×C59—21no—
86C4×D4×C59—21no—
87C4×D4×C59—21no—
88C4×D4×C59—21no—
89C4×D4×C59—21no—
90C4×D4×C59—21no—
91C4×D4×C59—48no—
92C4×D4×C59D412yescomplemented
93#117×C59—22no—
94#117×C59—22no—
95#117×C59—21no—
96C2×C4⋊C4×C59—22no—
97C2×C4⋊C4×C59—22no—
98C2×C4⋊C4×C59D411yescharacteristic
99C2×C4⋊C4×C59C2311yescharacteristic
100C2×C22⋊C4×C59—22no—
101C2×C22⋊C4×C59—21no—
102C2×C22⋊C4×C59—22no—
103C2×C22⋊C4×C59C2312yes—
104C2×C42×C59—21no—
105C2×C42×C59C2311yescharacteristic
106#107×C59—22no—
107#106×C59—22no—
108C4⋊C8×C59—21no—
109C4⋊C8×C59—21no—
110#103×C59—22no—
111#102×C59—22no—
112#102×C59—22no—
113#102×C59—22no—
114C22⋊C8×C59C2312yes—
115C22⋊C8×C59C2312yes—
116#97×C59—21no—
117#97×C59—21no—
118#95×C59—21no—
119#95×C59C2312yes—
120C24×C59—21no—
121C24×C59C2×D412yes—
122#41×C59—44no—
123#41×C59—84no—
124C2×Q8×C59—21no—
125C2×Q8×C59—21no—
126C2×Q8×C59C2×D412yes—
127C2×D4×C59—22no—
128C2×D4×C59—24no—
129C2×D4×C59—24no—
130C2×D4×C59—21no—
131C2×D4×C59—21no—
132C2×D4×C59—21no—
133C2×D4×C59—21no—
134C2×D4×C59—21no—
135C2×D4×C59—21no—
136C2×D4×C59—42no—
137C2×D4×C59—44no—
138C2×D4×C59—42no—
139C2×D4×C59—44no—
140C2×D4×C59—44no—
141C2×D4×C59C2×D412yes—
142C22×C4×C59—22no—
143C22×C4×C59—24no—
144C22×C4×C59—22no—
145C22×C4×C59—22no—
146C22×C4×C59—22no—
147C22×C4×C59—21no—
148C22×C4×C59—44no—
149C22×C4×C59—44no—
150C22×C4×C59—41no—
151C22×C4×C59—41no—
152C22×C4×C59C2×D411yescharacteristic
153C22×C4×C59C2×D411yescharacteristic
154C22×C4×C59C2×D412yes—
155C22×C4×C59C2411yescharacteristic
156SD16×C59—44no—
157D8×C59—44no—
158C2×C8×C59—22no—
159C2×C8×C59—22no—
160C4⋊C4×C59—24no—
161C4⋊C4×C59—21no—
162C4⋊C4×C59—21no—
163C4⋊C4×C59—21no—
164C4⋊C4×C59—21no—
165C4⋊C4×C59—21no—
166C4⋊C4×C59—21no—
167C4⋊C4×C59—22no—
168C4⋊C4×C59—22no—
169C4⋊C4×C59—21no—
170C4⋊C4×C59—21no—
171C4⋊C4×C59—44no—
172C4⋊C4×C59C2×D412yes—
173C4⋊C4×C59C2×D412yes—
174C22⋊C4×C59—24no—
175C22⋊C4×C59—24no—
176C22⋊C4×C59—24no—
177C22⋊C4×C59—22no—
178C22⋊C4×C59—22no—
179C22⋊C4×C59—22no—
180C22⋊C4×C59—22no—
181C22⋊C4×C59—22no—
182C22⋊C4×C59—44no—
183C22⋊C4×C59—44no—
184C22⋊C4×C59—41no—
185C22⋊C4×C59—41no—
186C42×C59—24no—
187C42×C59—24no—
188C42×C59—22no—
189C42×C59C2×D411yescharacteristic
190C42×C59C2×D411yescharacteristic
191C42×C59C2×D411yescharacteristic
192C42×C59C2×D411yescharacteristic
193C23×C59—22no—
194C23×C59—22no—
195C23×C59—22no—
196C23×C59—22no—
197C23×C59—22no—
198C23×C59—42no—
199C23×C59—42no—
200C23×C59—42no—
201C23×C59—41no—
202C23×C59—41no—
203C23×C59—42no—
204C23×C59C22×D411yescharacteristic
205Q8×C59—42no—
206Q8×C59—42no—
207Q8×C59—42no—
208D4×C59—22no—
209D4×C59—22no—
210D4×C59—42no—
211D4×C59—42no—
212D4×C59—42no—
213D4×C59—41no—
214D4×C59—41no—
215D4×C59—42no—
216D4×C59—416no—
217D4×C59—44no—
218D4×C59—42no—
219D4×C59—84no—
220D4×C59—84no—
221C2×C4×C59—22no—
222C2×C4×C59—22no—
223C2×C4×C59—24no—
224C2×C4×C59—22no—
225C2×C4×C59—22no—
226C2×C4×C59—22no—
227C2×C4×C59—22no—
228C2×C4×C59—41no—
229C2×C4×C59—44no—
230C2×C4×C59—42no—
231C2×C4×C59—42no—
232C2×C4×C59—44no—
233C2×C4×C59—42no—
234C2×C4×C59—42no—
235C2×C4×C59—41no—
236C2×C4×C59—82no—
237C2×C4×C59—82no—
238C2×C4×C59—84no—
239C2×C4×C59—82no—
240C2×C4×C59#12011yescharacteristic
241C2×C4×C59#12011yescharacteristic
242C2×C4×C59#12011yescharacteristic
243C2×C4×C59#12011yescharacteristic
244C2×C4×C59C22×D411yescharacteristic
245C2×C4×C59C22×D411yescharacteristic
246C8×C59—42no—
247C8×C59—42no—
248#18190C5911yesmaximal, characteristic, direct product factor, Sylow
249C22×C59—21no—
250C22×C59—21no—
251C22×C59—44no—
252C22×C59—44no—
253C22×C59—42no—
254C22×C59—42no—
255C22×C59—42no—
256C22×C59—42no—
257C22×C59—42no—
258C22×C59—42no—
259C22×C59—42no—
260C22×C59—82no—
261C22×C59—82no—
262C22×C59—81no—
263C22×C59—81no—
264C22×C59C2×#12011yescharacteristic
265C22×C59#57512yes—
266C4×C59—21no—
267C4×C59—21no—
268C4×C59—21no—
269C4×C59—21no—
270C4×C59—21no—
271C4×C59—44no—
272C4×C59—42no—
273C4×C59—42no—
274C4×C59—42no—
275C4×C59—42no—
276C4×C59—81no—
277C4×C59#45312yes—
278#3506C2×C5911yescharacteristic, complemented
279#3110C2×C5911yescharacteristic, complemented
280#3109C2×C5911yescharacteristic, complemented
281#2397C2×C5911yescharacteristic, complemented
282#1618C2×C5914yescomplemented
283#1600C2×C5914yescomplemented
284#1506C2×C5911yescharacteristic, complemented
285#1505C2×C5911yescharacteristic, complemented
286#1466C2×C5911yescharacteristic, complemented
287C2×C59—22no—
288C2×C59—82no—
289C2×C59—82no—
290C2×C59—82no—
291C2×C59#300511yescharacteristic
292C2×C59C2×#45311yescharacteristic
293C2×C59#302511yescharacteristic
294#559—22no—
295#556—21no—
296#555—21no—
297#553—22no—
298#550—21no—
299#547—21no—
300#538C22×C5914yes—
301#535—21no—
302#533C22×C5911yescharacteristic
303#532C22×C5911yescharacteristic
304#525—22no—
305#520—21no—
306C2×C4×D4—22no—
307C2×C4×D4C22×C5911yescharacteristic
308C2×C4×D4C22×C5911yescharacteristic
309#484C22×C5912yes—
310#481C22×C5912yes—
311#476—21no—
312#474—21no—
313#461—21no—
314#459—21no—
315#450C22×C5912yes—
316#447C22×C5912yes—
317#442—22no—
318#440—22no—
319#432C22×C5911yescharacteristic
320#432C22×C5911yescharacteristic
321#399—21no—
322#399C22×C5912yes—
323#392—21no—
324#392C22×C5912yes—
325#376C22×C5911yescharacteristic
326#328C22×C5914yes—
327#327C22×C5914yes—
328#323C22×C5914yes—
329C59#1819011yescharacteristic, direct product factor, Sylow
330C2×#41—22no—
331C2×#41—21no—
332C22×D4—22no—
333C22×D4D4×C5911yescharacteristic
334C22×D4C23×C5911yescharacteristic
335C23×C4—21no—
336C23×C4D4×C5912yes—
337C2×SD16—22no—
338C2×D8—22no—
339C4⋊Q8D4×C5911yescharacteristic, complemented
340C4⋊Q8D4×C5911yescharacteristic, complemented
341C4⋊Q8D4×C5911yescharacteristic, complemented
342#127—22no—
343#127D4×C5911yescharacteristic, complemented
344#126—24no—
345#125—21no—
346#124—22no—
347#124—24no—
348#124—21no—
349#123—24no—
350#123—24no—
351C22⋊Q8—22no—
352C22⋊Q8—21no—
353C22⋊Q8C23×C5912yes—
354#121—22no—
355#121—22no—
356#121—22no—
357#121—24no—
358#121—21no—
359#121C23×C5912yes—
360#120—24no—
361C4×Q8—22no—
362C4×Q8—21no—
363C4×Q8D4×C5912yescomplemented
364C4×D4—22no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—48no—
377C4×D4D4×C5912yescomplemented
378#117—22no—
379#117—22no—
380#117—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4D4×C5911yescharacteristic
384C2×C4⋊C4C23×C5911yescharacteristic
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4C23×C5912yes—
389C2×C42—21no—
390C2×C42C23×C5911yescharacteristic
391#107—22no—
392#106—22no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395#103—22no—
396#102—22no—
397#102—22no—
398#102—22no—
399C22⋊C8C23×C5912yes—
400C22⋊C8C23×C5912yes—
401#97—21no—
402#97—21no—
403#95—21no—
404#95C23×C5912yes—
405C24—21no—
406C24C2×D4×C5912yes—
407#41—44no—
408#41—84no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8C2×D4×C5912yes—
412C2×D4—22no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—42no—
422C2×D4—44no—
423C2×D4—42no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4C2×D4×C5912yes—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4C2×D4×C5911yescharacteristic
438C22×C4C2×D4×C5911yescharacteristic
439C22×C4C2×D4×C5912yes—
440C22×C4C24×C5911yescharacteristic
441SD16—44no—
442D8—44no—
443C2×C8—22no—
444C2×C8—22no—
445C4⋊C4—24no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—44no—
457C4⋊C4C2×D4×C5912yes—
458C4⋊C4C2×D4×C5912yes—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—44no—
468C22⋊C4—44no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C42—24no—
472C42—24no—
473C42—22no—
474C42C2×D4×C5911yescharacteristic
475C42C2×D4×C5911yescharacteristic
476C42C2×D4×C5911yescharacteristic
477C42C2×D4×C5911yescharacteristic
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—41no—
487C23—41no—
488C23—42no—
489C23C22×D4×C5911yescharacteristic
490Q8—42no—
491Q8—42no—
492Q8—42no—
493D4—22no—
494D4—22no—
495D4—42no—
496D4—42no—
497D4—42no—
498D4—41no—
499D4—41no—
500D4—42no—
501D4—416no—
502D4—44no—
503D4—42no—
504D4—84no—
505D4—84no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—84no—
524C2×C4—82no—
525C2×C4#120×C5911yescharacteristic
526C2×C4#120×C5911yescharacteristic
527C2×C4#120×C5911yescharacteristic
528C2×C4#120×C5911yescharacteristic
529C2×C4C22×D4×C5911yescharacteristic
530C2×C4C22×D4×C5911yescharacteristic
531C8—42no—
532C8—42no—
533C22—21no—
534C22—21no—
535C22—44no—
536C22—44no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—82no—
545C22—82no—
546C22—81no—
547C22—81no—
548C22C2×#120×C5911yescharacteristic
549C22C59×#57512yes—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—44no—
556C4—42no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—81no—
561C4C59×#45312yes—
562C2—22no—
563C2—82no—
564C2—82no—
565C2—82no—
566C2C59×#300511yescharacteristic
567C2C2×C59×#45311yescharacteristic
568C2C59×#302511yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C59×#3506C2semidirect
2. C59×#3110C2semidirect
3. C59×#3109C2semidirect
4. C59×#2397C2semidirect
5. C59×#1618C2semidirect
6. C59×#1600C2semidirect
7. C59×#1506C2semidirect
8. C59×#1505C2semidirect
9. C59×#1466C2semidirect
54. C4⋊Q8×C59D4semidirect
55. C4⋊Q8×C59D4semidirect
56. C4⋊Q8×C59D4semidirect
58. #127×C59D4semidirect
78. C4×Q8×C59D4semidirect
92. C4×D4×C59D4semidirect
248. #18190C59direct (N × H)
278. #3506C2×C59semidirect
279. #3110C2×C59semidirect
280. #3109C2×C59semidirect
281. #2397C2×C59semidirect
282. #1618C2×C59semidirect
283. #1600C2×C59semidirect
284. #1506C2×C59semidirect
285. #1505C2×C59semidirect
286. #1466C2×C59semidirect
329. C59#18190direct (N × H)
339. C4⋊Q8D4×C59semidirect
340. C4⋊Q8D4×C59semidirect
341. C4⋊Q8D4×C59semidirect
343. #127D4×C59semidirect
363. C4×Q8D4×C59semidirect
377. C4×D4D4×C59semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C59×#35062
C59×#31102
C59×#31092
C59×#23972
C59×#16182
C59×#16002
C59×#15062
C59×#15052
C59×#14662
#1819059